Codimensions of algebras with pseudoautomorphism and their exponential growth

Let F be a fixed field of characteristic zero containing an element i such that i² = -1. In this paper we consider finite dimensional superalgebras over F endowed with a pseudoautomorphism p and we investigate the asymptotic behaviour of the corresponding sequence of p-codimensions cₙᵖ(A), n=1,2, …. First we give a positive answer to a conjecture of Amitsur in this setting: the p-exponent expᵖ(A) = limn → ∞ √[n]cₙᵖ(A) always exists and it is an integer. In the final part we characterize the algebras whose exponential growth is bounded by $2$.